Abstract: To investigate the fundamental principles of H2 formation in a giant
molecular cloud (GMC), we derive the HI and H2 surface density (Sigma_HI and
Sigma_H2) images of the Perseus molecular cloud on sub-pc scales (~0.4 pc). We
use the far-infrared data from the Improved Reprocessing of the IRAS Survey and
the V-band extinction image provided by the COMPLETE Survey to estimate the
dust column density image of Perseus. In combination with the HI data from the
Galactic Arecibo L-band Feed Array HI Survey and an estimate of the local
dust-to-gas ratio, we then derive the Sigma_H2 distribution across Perseus. We
find a relatively uniform Sigma_HI ~ 6-8 Msun pc^-2 for both dark and
star-forming regions, suggesting a minimum HI surface density required to
shield H2 against photodissociation. As a result, a remarkably tight and
consistent relation is found between Sigma_H2/Sigma_HI and Sigma_HI+Sigma_H2.
The transition between the HI- and H2-dominated regions occurs at N(HI)+2N(H2)
~ (8-14) x 10^20 cm^-2. Our findings are consistent with predictions for H2
formation in equilibrium, suggesting that turbulence may not be of primary
importance for H2 formation. However, the importance of a warm neutral medium
for H2 shielding, an internal radiation field, and the timescale of H2
formation still remain as open questions. We also compare H2 and CO
distributions and estimate the fraction of "CO-dark" gas, f_DG ~ 0.3. While
significant spatial variations of f_DG are found, we do not find a clear
correlation with the mean V-band extinction.